APPLICATIONS OF NONLINEAR DYNAMICS TO TIME DEPENDENT THERMAL CONVECTION (BOUNDARY LAYER INSTABILITY)

Available from UMI in association with The British Library. Requires signed TDF.; Two types of chaotic behaviour exhibited by Rayleigh-Benard convection at high Prandtl number are discussed. These are boundary layer instabilities and the slow migration of thermal plumes.; The study of boundary layer instabilities is based on Howard's bubble model of convection. A model system of partial differential equations is derived from a boundary layer rescaling of the Boussinesq equations. In the limit of large Prandtl number multiple length scales are found within the boundary layer structure and these are analysed by asymptotic techniques. A combination of theoretical and numerical methods allow the construction of an infinite dimensional Poincare map. The dynamics of this map are investigated and related to irregular plume detachments in high Prandtl number fluids.; The slow migration of thermal plumes is modelled by a set of ordinary differential equations for variables describing the size and location of convection cells. The differential equations are derived using a quasi-stationary boundary layer theory for an infinite Prandtl number fluid. Numerical techniques are used to investigate up to three slowly moving plumes in both thin and moderate aspect ratio cells. Possible boundary layer instabilities occurring on a fast time scale are investigated and the results related to spoke patterned convection.